The Actinopterygii are the ray-finned fish. They are the dominant group of vertebrates, with over 27,000 species ubiquitous throughout freshwater and marine environments. They are traditionally treated as a subclass of the Osteichthyes, or bony fish, but as that group is paraphyletic they may be treated as a full class.

Traditionally three grades of Actinopterygii have been recognized: the Chondrostei, Holostei, and Teleostei. The second is paraphyletic and tends to be abandoned, however, while the first is now restricted to those forms closer to extant Chondrostei than to the other groups. Nearly all fish alive today are teleosts. A listing of the different groups is given below, down to the level of orders, arranged in what is believed to represent the evolutionary sequence down to the level of superorder.